AC16
Debris disks from grain collisions to thermal evidence
A dust grain changes its orbit when a collision changes its size. Connect that motion to a consistent thermal image, then ask what real observations can distinguish.
Concept
What a bright dust ring can tell us about an unseen planet
Dust can carry a planet’s dynamical imprint, but temperature, collisions and resolution can produce competing explanations.
L1
From a collision to a new dust orbit
Derive the radiation-to-gravity ratio, the circular-release escape threshold and a conditional steady-cascade slope.
L2
Couple a fragment mass budget to orbital transport
Write the star-centered force, unordered collision rates, finite fragment integrals and the numerical error ledger.
L3
Turn one grain record into a thermal image and spectrum
Derive radiative equilibrium, spectral flux, sky projection and beam units from one physical grain population.
Tutorial
Fit a real SMA image and infrared spectrum without inventing a planet
Rerun a standard-library Python fit to fixed HD 48682 data, preserve beam units and compare radius–grain degeneracies.
L4 · Paper guide
Read ARKS without turning every dust arc into a planet
Read fixed ARKS II/VI sections and figures, separate image evidence from dynamical assumptions, and plan a falsifiable follow-up.
Three textbook chapters connect grain forces, collision mass flow and thermal observation. A public Python exercise preserves actual SMA and infrared inputs. The final guide separates ARKS image features from the dynamical assumptions needed to interpret them.
Sources and calculation scope
- Stark & Kuchner 2009 · collisional grooming, fixed arXiv 0909.2227v1
Primary full text: sections II.1–II.4, III and IV; local rates, grid/noise tests and the limits of fragment reassignment. This weighted initial-value operator is not a reproduction of their steady-stream solver.
- REBOUNDx 5.1.0 · radiation forces and physical light speed
Official force documentation and example; independent records use actual REBOUND 5.2.2 IAS15 plus REBOUNDx 5.1.0, with physical-c PR and barycentric coordinates converted to the star frame.
- Matrà · REASONS archive 12583396, version v0.0, CC BY 4.0
Original unchanged HD 48682 restored SMA FITS and fit notes; image units and actual beam retained. The filename does not make it a visibility table. Source-paper context: arXiv 2501.09058v1, 15 January 2025, A&A 693 A151.
- Hengst et al. 2020 · HD 48682, Tables 1–2
Published stellar values and six numerical cold-photometry detections; one PACS reduction only. Unverified upper-limit conventions and correlated synthetic spectral bins are excluded.
- Hengst et al. 2020 · published erratum
9 October 2020 correction and expanded SMA observing/calibration description. The delivered REASONS product remains separately versioned; no reduction pipeline was rerun.
- Han et al. · ARKS II, arXiv 2601.13670v1
Fixed 20 January 2026 full-text target, published A&A 705 A196. Close reading: sections 2 and 4.3–4.5, Figure 8 and Appendix H. No ARKS data reproduction or planet discovery is claimed.
- Lovell et al. · ARKS VI, arXiv 2601.11766v1
Fixed 16 January 2026 full-text target, published A&A 705 A200. Close reading: sections 2.2, 3.1.7–3.1.10 and 4.1–4.2, and Figure 6. The gas-rich alternatives lie outside the gas-free Lab.
- Dohnanyi 1968 · NASA-CR-99280, sections III–IV and Table III
Public original report dated 22 July 1968; section IV and Table III distinguish the ideal eleven-sixths mass slope from numerical collision-model slopes. The later journal paper is JGR 74, 2531–2554, 15 May 1969, DOI 10.1029/JB074i010p02531. This course derives a restricted scale-free limit.